Question

The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

Weekly Gross Revenue ($1,000s)	Television Advertising ($1,000s)	Newspaper Advertising ($1,000s)
96	5	1.5
91	2	2
95	4	1.5
93	2.5	2.5
95	3	3.3
94	3.5	2.3
94	2.5	4.1
94	3	2.5

(a)Use α = 0.01 to test the hypotheses

H0:	β1 = β2 = 0
Ha:	β1 and/or β2 is not equal to zero

for the model y = β₀ + β₁x₁ + β₂x₂ + ε,  where

x1	=	television advertising ($1,000s)
x2	=	newspaper advertising ($1,000s).

Find the value of the test statistic. (Round your answer to two decimal places.)

(b) Use α = 0.05 to test the significance of β₁.

Find the value of the test statistic. (Round your answer to two decimal places.)

(c)Use α = 0.05 to test the significance of β₂.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Answer 1

Applying regression from excel :data-data analysis: regression:

Regression Statistics
Multiple R	0.961998
R Square	0.92544
Adjusted R Square	0.895616
Standard Error	0.488459
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	14.80704	7.403519	31.03	0.001518
Residual	5	1.192962	0.238592
Total	7	16
	Coefficients	Standard Error	t Stat	P-value
Intercept	85.7635	1.216266	70.51379	0.0000
x1	1.823114	0.232126	7.853989	0.000537
x2	0.984903	0.252228	3.904815	0.011354

a)

value of the test statistic =31.03

p value =0.002

b) value of the test statistic =7.85

p value =0.001

c)

value of the test statistic =3.90

p value =0.011